CN101976846A - STATCOM (static compensator) control method based on switching system theory - Google Patents

Abstract

The invention provides a STATCOM (static compensator) control method based on a switching system theory, which comprises the following steps of: analyzing a main circuit topological structure of an STATCOM device, and determining a mathematical model of a singe unit-infinite system comprising a STATCOM, determining a three-order model of a generator in the singe unit-infinite system comprising the STATCOM, and a state equation and an output equation of an electric power system comprising the STATCOM; linearizing a nonlinear model of the STATCOM; determining the design steps of an H infinity robust controller mathematical model of the STATCOM and a generator excitation robust controller; and determining the structural composition of the whole system of the STATCOM based on a DSP (Digital Signal Processor). A controller designed according to the method of the invention can ensure that the system is stabilized on one hand when the system fails, and can eliminate the influence of the interference on the performance of the system on the other hand.

Description

STATCOM control method based on the switched system theory

[technical field]:

The invention belongs to power electronic technology and robust control technique field, relate to the control strategy of a kind of novel advanced person's static var compensator (STATCOM) based on DSP, utilize the Decentralized Robust Control theory, and from unit-its dynamic process of Infinite bus system research of STATCOM, set up the STATCOM dynamic model and the differential equation that contains STATCOM power system dynamic states model, design the H of STATCOM _∞Robust controller and Robust Controller for Excitation of Generator.

[background technology]:

At present the research of static var compensator (STATCOM) is mainly concentrated on main wiring mode and topological structure, system modelling, system control method and it aspects such as effect to stability of power system.First STATCOM commercial plant that adopts GTO in the world by US Westinghouse company's development, use a plurality of inverters to be connected with the voltage electrical network by tortuous transformer or common transformer, waveform phase shift stack with a plurality of inverter outputs, obtain being similar to sine-shaped three symmetrical output voltages, the STATCOM commercial plant that puts into operation both at home and abroad later all adopts above-mentioned identical main circuit structure, is called as multiple inverter configuration.Multiple inverter configuration not only is issued to the purpose of aggrandizement apparatus capacity in the condition of the equal flow problem of having avoided the device parallel connection, while approaches sine wave by means of the method that the square-wave signal with several current transformers outputs is combined into staircase waveform, can be issued to the purpose that suppresses harmonic wave in the condition that does not improve switching frequency again, therefore in high-power converter, be used widely.Though this structure is very effective owing to need the tortuous transformer of particular design, both improved cost, the complexity that system is become, and each mutually between complicated electromagnetic coupled also make the phase-splitting control when asymmetric difficulty that becomes.

Continuous development along with power electronic technology, big capacity device continues to bring out, above-mentioned main circuit structure complicated problems should be not difficult to be resolved, promptly might constitute the STATCOM of suitable capacity with single inverter, utilize pulse-width modulation (PWM) technology to produce the sinusoidal output voltage of required power frequency simultaneously.At present, in the STATCOM main circuit, the main flow structure that is adopted is voltage source inverter (VSI), but also there is the researcher to carry out, to having carried out Primary Study based on the dynamic model of the STATCOM of current source inverter, steady-state behaviour, Control System Design etc. to the application study of current source inverter (CSI) in STATCOM.The STATCOM device can be regarded as and connects a controlled reactive power source with system.Set up one suitable, can reflect in detail that the Mathematical Modeling of STATCOM character is that device is control effectively, and then bring into play the basis that it should have effect.

[summary of the invention]:

The present invention seeks to overcome the prior art above shortcomings, a kind of STATCOM control method based on the switched system theory is provided.This method is with the core content of STATCOM control strategy for studying based on the switched system theory, the characteristics and the requirement of user that increase rapidly according to the non-linear load or burden without work of present electric power system to improving constantly with electricity quality, at present STATCOM deficiency in actual applications, be devoted to set up unit-Infinite bus system Mathematical Modeling of a kind of STATCOM and control effectively, and emphatically the control method for coordinating of the foundation of the Mathematical Modeling of STATCOM and STATCOM control system design and based on the design of Controller of DSP.

STATCOM control method based on the switched system theory provided by the invention comprises:

1st, analyze the main circuit topological structure of STATCOM device, determine to comprise the Mathematical Modeling of unit-Infinite bus system of STATCOM;

2nd, determine to comprise the third-order model of generator in unit-Infinite bus system of STATCOM, and the power system state equation and the output equation that contain STATCOM;

3rd, with the nonlinear model linearisation of STATCOM;

4th, determine the H of STATCOM _∞The design procedure of robust controller Mathematical Modeling and Robust Controller for Excitation of Generator;

5th, determine to form based on the structure of the The whole control system of the STATCOM of DSP.

The Mathematical Modeling of unit-Infinite bus system of the described STATCOM of comprising is:

$\left\{\begin{array}{c}\stackrel{.}{\mathrm{\δ}}=\mathrm{\ω}\\ M\stackrel{.}{\mathrm{\ω}}+\mathrm{D\ω}=P_m-(\frac{E_q^2}{X_L}\sin \mathrm{\δ}-\frac{1}{2}{E}_q{I}_{\mathrm{CR}}\sin \frac{\mathrm{\δ}}{2})\end{array}\right.$

In the formula, δ is a generator's power and angle, and ω is a rotor velocity, P _mBe generator input mechanical output, E _qHand over the axle electromotive force for generator, D is the unit damping constant, and M is an inertia constant of a set, X _LBe line reactance, I _CRBe the reactive power compensation electric current.

The third-order model of described generator is:

$\left\{\begin{array}{c}\stackrel{.}{\mathrm{\δ}}=\mathrm{\ω}\\ \stackrel{.}{\mathrm{\ω}}=-\frac{D}{M}\mathrm{\ω}+\frac{{\mathrm{\ω}}_0}{M}(P_m-P_e)\\ E_q^{\′}=-\frac{1}{T_{d0}^{\′}}{E}_q+\frac{1}{T_{d0}^{\′}}{E}_f\end{array}\right.$

In the formula, δ is a generator's power and angle, and ω is a rotor velocity, P _mBe generator input mechanical output, P _eBe generator active power, D is the unit damping constant, and M is an inertia constant of a set, E ' _qFor generator is handed over axle (q-axle) transient potential, E _qFor generator is handed over axle electromotive force, E _fBe generator excitation winding equivalent potential, T ' _DoBe d-axis transient state open circuit time constant.

Power system state equation and the output equation of the described STATCOM of containing are respectively:

Make system mode vector x=[x ₁x ₂x ₃] ^T=[δ ω E ' _q] ^T, the input u=u of system _f, system exports y=δ, can draw the state equation of system:

$\stackrel{.}{x}=f\left(x\right)+g\left(x\right)u$

F (x)=[f wherein ₁(x) f ₂(x) f ₃(x)] ^T, g (x)=[0 0 g ₃] ^T

f ₁(x)＝x ₂， $f_2\left(x\right)=-\frac{D}{M}{x}_2+\frac{{\mathrm{\ω}}_0}{M}(P_m-\frac{V_1}{x_{\mathrm{d\Σ}}^{\′}}{x}_3\sin x_1)$

$f_3\left(x\right)=-\frac{1}{T_{\mathrm{do}}^{\′}}[x_3-(X_d-X_d^{\′})\frac{x_3-V_1\cos x_1}{X_{\mathrm{d\Σ}}^{\′}}],$ $g_3=\frac{k_c}{T_{d0}^{\′}};$

The output equation of system is:

y＝h(x)＝x ₁。

Model after the nonlinear model linearisation of described STATCOM is:

${\stackrel{.}{z}}_{123}={\mathrm{Az}}_{123}+B_{2}v+B_1{w}^{\′}$

${\stackrel{.}{z}}_4=a(z_{123},z_4)+b\left(w\right)$

y＝Cz ₁₂₃

Z wherein ₁₂₃=[z ₁z ₂z ₃] ^T, v=[v ₁v ₂] ^T, w '=[w ₁W ' ₂] ^T=[w ₁W ' ₂(w ₁, w ₂)] ^T

The H of described STATCOM _∞The robust controller Mathematical Modeling is:

$v_{1*}=-\frac{1}{{2\mathrm{\ϵ}}^2}\underset{i=1}{\overset{4}{\mathrm{\Σ}}}{p}_{2i}{z}_i,$ $v_{2*}=-\frac{1}{2{\mathrm{\ϵ}}^2}\underset{i=1}{\overset{4}{\mathrm{\Σ}}}{p}_{i4}{z}_i.$

The design procedure of described Robust Controller for Excitation of Generator is:

Step 1, the state-space model that provides system such as following formula formula (1) are described its uncertainty to (4), and analyze the uncertain boundary that it satisfies;

v _f＝I _q[k _cu _f-(X _d-X′ _d)I _d]+T′ _doQ _eω-P _m (2)

In the formula

$\mathrm{\μ}\left(t\right)=\frac{1}{{T^{\′}}_{d0}}-\frac{1}{{T^{\′}}_{d0}+{{\mathrm{\ΔT}}^{\′}}_{d0}},$ ${T^{\′}}_{d0}+{T^{\′}}_{d0}=\frac{{X^{\′}}_{\mathrm{d\Σ}}+{\mathrm{\ΔX}}_L}{X_{\mathrm{d\Σ}}+{\mathrm{\ΔX}}_L}{T}_{d0}$

Δ T ' _D0With Δ X _LRepresent T ' respectively _D0And X _LIn uncertainty, simultaneously, have

$T=\frac{{V^2}_t}{X_{\mathrm{d\Σ}}},$ $T+\mathrm{\ΔT}=\frac{{(V_t+{\mathrm{\ΔV}}_t)}^2}{{X^{\′}}_{\mathrm{d\Σ}}}$

Can be able to the lower linear model thus

$\stackrel{.}{\mathrm{\δ}}\left(t\right)=\mathrm{\ω}\left(t\right)$

$\stackrel{.}{\mathrm{\ω}}\left(t\right)=-\frac{D}{M}\mathrm{\ω}\left(t\right)-\frac{{\mathrm{\ω}}_0}{M}{\mathrm{\ΔP}}_e\left(t\right)$

$\mathrm{\Δ}{\stackrel{\·}{P}}_e\left(t\right)=-[\frac{1}{{T^{\′}}_{d0}}+\mathrm{\μ}\left(t\right)]{\mathrm{\ΔP}}_e\left(t\right)+[\frac{1}{{T^{\′}}_{d0}}+\mathrm{\μ}\left(t\right)]v_f\left(t\right)+[\frac{1}{{T^{\′}}_{d0}}+\mathrm{\μ}\left(t\right)]{{\mathrm{\ΔT}}^{\′}}_{d0}{Q}_e\left(t\right)\mathrm{\ω}\left(t\right)+(T+\mathrm{\ΔT})\mathrm{\ω}\left(t\right)+({E^{\′}}_q{V}_t/{{\stackrel{\·}{X}}^{\′}}_{d0})\sin \mathrm{\δ}\left(t\right)$

Definition status vector x (t)=[δ (t) ω (t) Δ P _e(t)] ^T, and the suffered interference w=[w of taking into account system model ₁w ₂] ^T, above-mentioned inearized model can be write as

$\stackrel{\·}{x}\left(t\right)[A+\mathrm{\ΔA}]x\left(t\right)+[B_2+{\mathrm{\ΔB}}_2]v_f\left(t\right)+B_{1}w\left(t\right)+\mathrm{\ΔGg}\left(x\right)---\left(4\right)$

z＝Cx (5)

Wherein

$A=\left(\begin{array}{ccc}0& 1& 0\\ 0& -\frac{D}{M}& -\frac{{\mathrm{\ω}}_0}{M}\\ 0& 0& -\frac{1}{{T^{\′}}_{d0}}\end{array}\right),\mathrm{\ΔA}=\left(\begin{array}{ccc}0& 0& 0\\ 0& 0& 0\\ 0& \mathrm{\β}& -\mathrm{\μ}\left(t\right)\end{array}\right),C=I$

$B_2={\left[\begin{array}{ccc}0& 0& \frac{1}{{T^{\′}}_{d0}}\end{array}\right]}^T,{\mathrm{\ΔB}}_2={\left[\begin{array}{ccc}0& 0& \mathrm{\μ}\left(t\right)\end{array}\right]}^T,B_1={\left[\begin{array}{ccc}0& 1& 0\\ 0& 0& 1\end{array}\right]}^T---\left(6\right)$

$\mathrm{\β}=[\frac{1}{{T^{\′}}_{d0}}+\mathrm{\μ}\left(t\right)]{{\mathrm{\ΔT}}^{\′}}_{d0}{Q}_e+(T+\mathrm{\ΔT})---\left(7\right)$

$\mathrm{\ΔG}={\left[\begin{array}{ccc}0& 0& \mathrm{\γ}\end{array}\right]}^T,\mathrm{\γ}=\frac{{E^{\′}}_q{\stackrel{\·}{V}}_t}{{X^{\′}}_{\mathrm{d\Σ}}},g\left(x\right)=\sin \mathrm{\δ}---\left(8\right)$

μ (t), Δ T, Δ T ' _D0Bounded, thereby β also is a bounded.By above processing, the dynamic model that comprises the generator in unit-infinitely great electric power system of STATCOM has changed into one and has comprised multiple probabilistic linear system, promptly mixes uncertain system.These uncertainties comprise Δ A, Δ B ₂The expression parameter uncertainty, by B ₁The disturbance uncertainty of expression, and the interconnected uncertainty of representing by Δ G.

Step 2, uncertain matrix is carried out STRUCTURE DECOMPOSITION;

These uncertainties can be done following decomposition

ΔA(t)＝LF(t)E ₁(9)

ΔB ₂(t)＝LF(t)E ₂(10)

ΔG(t)＝L′F′(t)E′(11)

Wherein

$\left.\begin{array}{c}L={\left[\begin{array}{ccc}0& 0& {\left|\mathrm{\μ}\right|}_{\max }\end{array}\right]}^{T}F\left(t\right)=\left[\begin{array}{ccc}0& \frac{\mathrm{\β}}{{\left|\mathrm{\β}\right|}_{\max }}& -\frac{\mathrm{\μ}}{{\left|\mathrm{\μ}\right|}_{\max }}\end{array}\right]\\ E_1=\mathrm{diag}\{1,\frac{{\left|\mathrm{\β}\right|}_{\max }}{{\left|\mathrm{\μ}\right|}_{\max }},1\},E_2={\left[\begin{array}{ccc}0& 0& -1\end{array}\right]}^T\\ L^{\′}={\left[\begin{array}{ccc}0& 0& {\left|\mathrm{\γ}\right|}_{\max }\end{array}\right]}^T,F^{\′}\left(t\right)=\left[\frac{\mathrm{\γ}}{{\left|\mathrm{\γ}\right|}_{\max }}\right],E^{\′}=\left[1\right]\end{array}\right\}---\left(12\right)$

Satisfy following uncertain boundary

F ^T(t)F(t)≤I，F′ ^T(t)F ^T(t)≤I (13)

And || g (x) ||≤|| Wx||, W=[1 0 0] (14)

And

Consider the effect of generator forced exciting in addition, under severe case, excitation ceiling voltage multiple is 5, can get

$\left|\mathrm{\γ}\right|\≤\frac{4}{{T^{\′}}_{d0}{|}_{\min }}{P}_e{|}_{\max }---\left(16\right)$

Step 3, the suitable symmetric positive definite matrix Q of selection, structure algebraically Riccati equation;

$A^{T}P+\mathrm{PA}+P(B_1{B}_1^T+r^{-2}{\mathrm{LL}}^T+{\mathrm{\λ}}^{-2}{L}^{\′}{L}^{\′T})P+r^2{E}_1^T{E}_1+W^{T}W+C^{T}C$

$-r^{-2}{(B_2^{T}P+E_2^T{E}_1)}^T{R}^{-1}(B_2^{T}P+E_2^T{E}_1)+Q=0$

Step 4, respectively according to 0＜r, λ＜1 and λ ²E ' ^TThe principle of E '＜I is selected parameter r, λ, and at this moment, Riccati equation is separated;

Step 5: find the solution Riccati equation, get its steady-state solution P, can obtain the robust controller of system.

Structural group prejudice Fig. 1 of the The whole control system of described STATCOM control method based on the switched system theory.

Operation principle of the present invention:

The operation principle of STATCOM control method based on the switched system theory involved in the present invention is: power electronic device produces the trigger impulse of certain rule, after amplifying, gate drive circuit goes to control the turn-on and turn-off of IGBT, make STATCOM produce correct output voltage, according to the lock-out pulse that obtains from the electrical network sampling, produce the pulse signal synchronous with line voltage, output voltage and line voltage that STATCOM is produced keep synchronously, thereby STATCOM can be incorporated into the power networks exactly, control STATCOM output voltage makes with line voltage and keeps certain phase angle and control modulation degree, thereby accurately controls the reactive power output of STATCOM.Simultaneously; carry out high-rise defencive function, transship or other abnormal state when STATCOM operates in, and electric current surpasses when protecting the setting value that moves; controller makes STATCOM get back to normal operating conditions by defencive function; avoid STATCOM low layer protection action, make its operate as normal continuously, in case mistake appears in some element of controller itself; controller can be found and report to the police; simultaneously do not make device out of service fully, after the fault restoration, can resume operation at an easy rate.

Advantage of the present invention and good effect:

According to the controller of the inventive method design, when system breaks down, can make system stability on the one hand, can eliminate the influence of interference on the other hand to systematic function.

[description of drawings]:

Fig. 1 is a STATCOM control system structure composition frame chart.

Fig. 2 is a H ∞ standard control schematic diagram.

Fig. 3 is the TMS320F240 architectural schematic.

Fig. 4 is the TMS320F240 module diagram.

[embodiment]:

Embodiment 1: a kind of STATCOM control method based on the switched system theory, and this method may further comprise the steps:

Steps A: analyze the main circuit topological structure of STATCOM device, determine to comprise the Mathematical Modeling of unit-Infinite bus system of STATCOM.

Step B: determine the third-order model of generator in the system and contain STATCOM power system state equation, output equation.

Step C: with the nonlinear model linearisation of STATCOM.

Step D: the H that determines STATCOM _∞The design procedure of robust controller Mathematical Modeling and Robust Controller for Excitation of Generator.

Step e: determine to form based on the structure (referring to Fig. 1) of the The whole control system of the STATCOM of DSP.

The Mathematical Modeling of appealing unit-Infinite bus system of said STATCOM is:

$\left\{\begin{array}{c}\stackrel{.}{\mathrm{\δ}}=\mathrm{\ω}\\ M\stackrel{.}{\mathrm{\ω}}+\mathrm{D\ω}=P_m-(\frac{E_q^2}{X_L}\sin \mathrm{\δ}-\frac{1}{2}{E}_q{I}_{\mathrm{CR}}\sin \frac{\mathrm{\δ}}{2})\end{array}\right.$

In the formula, E _qHand over the axle electromotive force for generator, δ is a generator's power and angle, and ω is a generator amature angular speed, and M is an inertia constant of a set, and D is the unit damping coefficient.

The third-order model of above-mentioned said generator is:

$\left\{\begin{array}{c}\stackrel{.}{\mathrm{\δ}}=\mathrm{\ω}\\ \stackrel{.}{\mathrm{\ω}}=-\frac{D}{M}\mathrm{\ω}+\frac{{\mathrm{\ω}}_0}{M}(P_m-P_e)\\ E_q^{\′}=-\frac{1}{T_{d0}^{\′}}{E}_q+\frac{1}{T_{d0}^{\′}}{E}_f\end{array}\right.$

In the formula, δ is a generator's power and angle, and ω is a rotor velocity, P _mBe generator input mechanical output, P _eBe generator active power, D is the unit damping constant, and M is an inertia constant of a set, E ' _qFor generator is handed over axle (q-axle) transient potential, E _qBe generator q-axle electromotive force, E _fBe generator excitation winding equivalent potential, T ' _DoBe d-axis transient state open circuit time constant.

Above-mentioned said state equation, output equation are respectively:

Make system mode vector x=[x ₁x ₂x ₃] ^T=[δ ω E ' _q] ^T, the input u=u of system _f, the output y=δ of system can draw system state equation:

$\stackrel{.}{x}=f\left(x\right)+g\left(x\right)u$

F (x)=[f wherein ₁(x) f ₂(x) f ₃(x)] ^T, g (x)=[0 0 g ₃] ^T

$f_1\left(x\right)=x_2,f_2\left(x\right)=-\frac{D}{M}{x}_2+\frac{{\mathrm{\ω}}_0}{M}(P_m-\frac{V_1}{x_{\mathrm{d\Σ}}^{\′}}{x}_3\sin x_1)$

$f_3\left(x\right)=-\frac{1}{T_{\mathrm{do}}^{\′}}[x_3-(X_d-X_d^{\′})\frac{x_3-V_1\cos x_1}{X_{\mathrm{d\Σ}}^{\′}}],$ $g_3=\frac{k_c}{T_{d0}^{\′}}$

Output equation is:

y＝h(x)＝x ₁

Model after the above-mentioned said linearisation is:

${\stackrel{.}{z}}_{123}={\mathrm{Az}}_{123}+B_{2}v+B_1{w}^{\′}$

${\stackrel{.}{z}}_4=a(z_{123},z_4)+b\left(w\right)$

y＝Cz ₁₂₃

Z wherein ₁₂₃=[z ₁z ₂z ₃] ^T, v=[v ₁v ₂] ^T, w '=[w ₁W ' ₂] ^T=[w ₁W ' ₂(w ₁, w ₂)] ^T.

The H of above-mentioned said STATCOM _∞The robust controller Mathematical Modeling is:

$v_{1*}=-\frac{1}{{2\mathrm{\ϵ}}^2}\underset{i=1}{\overset{4}{\mathrm{\Σ}}}{p}_{2i}{z}_i,$ $v_{2*}=-\frac{1}{2{\mathrm{\ϵ}}^2}\underset{i=1}{\overset{4}{\mathrm{\Σ}}}{p}_{i4}{z}_i$

The design procedure of Robust Controller for Excitation of Generator is:

Step 1, the state-space model that provides system such as following formula (1-4) are described its uncertainty, and analyze the uncertain boundary that it satisfies;

v _f＝I _q[k _cu _f-(X _d-X′ _d)I _d]+T′ _doQ _eω-P _m (2)

In the formula

$\mathrm{\μ}\left(t\right)=\frac{1}{{T^{\′}}_{d0}}\frac{1}{{T^{\′}}_{d0}+{{\mathrm{\ΔT}}^{\′}}_{d0}},$ ${T^{\′}}_{d0}+{T^{\′}}_{d0}=\frac{{X^{\′}}_{\mathrm{d\Σ}}+{\mathrm{\ΔX}}_L}{X_{\mathrm{d\Σ}}+{\mathrm{\ΔX}}_L}{T}_{d0}$

Δ T ' _D0With Δ X _LRepresent T ' respectively _D0And X _LIn uncertainty, simultaneously, have

$T=\frac{{V^2}_t}{X_{\mathrm{d\Σ}}},$ $T+\mathrm{\ΔT}=\frac{{(V_t+{\mathrm{\ΔV}}_t)}^2}{{X^{\′}}_{\mathrm{d\Σ}}}$

Can be able to the lower linear model thus

$\stackrel{.}{\mathrm{\δ}}\left(t\right)=\mathrm{\ω}\left(t\right)$

$\stackrel{.}{\mathrm{\ω}}\left(t\right)=-\frac{D}{M}\mathrm{\ω}\left(t\right)-\frac{{\mathrm{\ω}}_0}{M}{\mathrm{\ΔP}}_e\left(t\right)$

$\mathrm{\Δ}{\stackrel{\·}{P}}_e\left(t\right)=-[\frac{1}{{T^{\′}}_{d0}}+\mathrm{\μ}\left(t\right)]{\mathrm{\ΔP}}_e\left(t\right)+[\frac{1}{{T^{\′}}_{d0}}+\mathrm{\μ}\left(t\right)]v_f\left(t\right)+[\frac{1}{{T^{\′}}_{d0}}+\mathrm{\μ}\left(t\right)]{{\mathrm{\ΔT}}^{\′}}_{d0}{Q}_e\left(t\right)\mathrm{\ω}\left(t\right)+(T+\mathrm{\ΔT})\mathrm{\ω}\left(t\right)+({E^{\′}}_q{V}_t/{{\stackrel{\·}{X}}^{\′}}_{d0})\sin \mathrm{\δ}\left(t\right)$

Definition status vector x (t)=[δ (t) ω (t) Δ P _e(t)] ^T, and the suffered interference of taking into account system model

W=[w ₁w ₂] ^T, above-mentioned inearized model can be write as

$\stackrel{\·}{x}\left(t\right)[A+\mathrm{\ΔA}]x\left(t\right)+[B_2+{\mathrm{\ΔB}}_2]v_f\left(t\right)+B_{1}w\left(t\right)+\mathrm{\ΔGg}\left(x\right)---\left(4\right)$

z＝Cx (5)

Wherein

$A=\left(\begin{array}{ccc}0& 1& 0\\ 0& -\frac{D}{M}& -\frac{{\mathrm{\ω}}_0}{M}\\ 0& 0& -\frac{1}{{T^{\′}}_{d0}}\end{array}\right),\mathrm{\ΔA}=\left(\begin{array}{ccc}0& 0& 0\\ 0& 0& 0\\ 0& \mathrm{\β}& -\mathrm{\μ}\left(t\right)\end{array}\right),C=I$

$B_2={\left[\begin{array}{ccc}0& 0& \frac{1}{{T^{\′}}_{d0}}\end{array}\right]}^T,{\mathrm{\ΔB}}_2={\left[\begin{array}{ccc}0& 0& \mathrm{\μ}\left(t\right)\end{array}\right]}^T,B_1={\left[\begin{array}{ccc}0& 1& 0\\ 0& 0& 1\end{array}\right]}^T---\left(6\right)$

$\mathrm{\β}=[\frac{1}{{T^{\′}}_{d0}}+\mathrm{\μ}\left(t\right)]{{\mathrm{\ΔT}}^{\′}}_{d0}{Q}_e+(T+\mathrm{\ΔT})---\left(7\right)$

$\mathrm{\ΔG}={\left[\begin{array}{ccc}0& 0& \mathrm{\γ}\end{array}\right]}^T,\mathrm{\γ}=\frac{{E^{\′}}_q{\stackrel{\·}{V}}_t}{{X^{\′}}_{\mathrm{d\Σ}}},g\left(x\right)=\sin \mathrm{\δ}---\left(8\right)$

μ (t), Δ T, Δ T ' _D0Bounded, thereby β also is a bounded.By above processing, the dynamic model that comprises the generator in unit-infinitely great electric power system of STATCOM has changed into one and has comprised multiple probabilistic linear system, promptly mixes uncertain system.These uncertainties comprise Δ A, Δ B ₂The expression parameter uncertainty, by B ₁The disturbance uncertainty of expression, and the interconnected uncertainty of representing by Δ G.

Step 2, uncertain matrix is carried out STRUCTURE DECOMPOSITION;

These uncertainties can be done following decomposition

ΔA(t)＝LF(t)E ₁(9)

ΔB ₂(t)＝LF(t)E ₂(10)

ΔG(t)＝L′F′(t)E′(11)

Wherein

$\left.\begin{array}{c}L={\left[\begin{array}{ccc}0& 0& {\left|\mathrm{\μ}\right|}_{\max }\end{array}\right]}^{T}F\left(t\right)=\left[\begin{array}{ccc}0& \frac{\mathrm{\β}}{{\left|\mathrm{\β}\right|}_{\max }}& -\frac{\mathrm{\μ}}{{\left|\mathrm{\μ}\right|}_{\max }}\end{array}\right]\\ E_1=\mathrm{diag}\{1,\frac{{\left|\mathrm{\β}\right|}_{\max }}{{\left|\mathrm{\μ}\right|}_{\max }},1\},E_2={\left[\begin{array}{ccc}0& 0& -1\end{array}\right]}^T\\ L^{\′}={\left[\begin{array}{ccc}0& 0& {\left|\mathrm{\γ}\right|}_{\max }\end{array}\right]}^T,F^{\′}\left(t\right)=\left[\frac{\mathrm{\γ}}{{\left|\mathrm{\γ}\right|}_{\max }}\right],E^{\′}=\left[1\right]\end{array}\right\}---\left(12\right)$

Satisfy following uncertain boundary

F ^T(t)F(t)≤I，F′ ^T(t)F ^T(t)≤I (13)

And || g (x) ||≤|| Wx||, W=[1 0 0] (14)

And

Consider the effect of generator forced exciting in addition, under severe case, excitation ceiling voltage multiple is 5, can get

$\left|\mathrm{\γ}\right|\≤\frac{4}{{T^{\′}}_{d0}{|}_{\min }}{P}_e{|}_{\max }---\left(16\right)$

Step 3, the suitable symmetric positive definite matrix Q of selection, structure algebraically Riccati equation;

$A^{T}P+\mathrm{PA}+P(B_1{B}_1^T+r^{-2}{\mathrm{LL}}^T+{\mathrm{\λ}}^{-2}{L}^{\′}{L}^{\′T})P+r^2{E}_1^T{E}_1+W^{T}W+C^{T}C$

$-r^{-2}{(B_2^{T}P+E_2^T{E}_1)}^T{R}^{-1}(B_2^{T}P+E_2^T{E}_1)+Q=0$

Step 4, respectively according to 0＜r, λ＜1 and λ ²E ' ^TThe principle of E '＜I is selected parameter r, λ, and at this moment, Riccati equation is separated;

Step 5: find the solution Riccati equation, get its steady-state solution P, can obtain the robust controller of system.

Structural group prejudice Fig. 1 of the The whole control system of above-mentioned said STATCOM control device based on the switched system theory.

Control system shown in Figure 1 is mainly finished following task: (1) produces the trigger impulse of certain rule, goes to control the turn-on and turn-off of IGBT after gate drive circuit amplifies, and is that STATCOM produces correct output voltage; (2) according to the lock-out pulse that obtains from the electrical network sampling, produce the pulse signal synchronous with line voltage, output voltage and line voltage that STATCOM is produced keep synchronously, thereby STATCOM can be incorporated into the power networks exactly; (3) control STATCOM output voltage makes with line voltage and keeps certain phase angle and control modulation degree, thereby accurately controls the reactive power output of STATCOM; (4) carry out high-rise defencive function.Promptly, STATCOM transships or other abnormal state when operating in, and electric current surpasses when protecting the setting value that moves, controller makes STATCOM get back to normal operating conditions by defencive function, avoids STATCOM low layer protection action, makes its operate as normal continuously; (5) in case mistake appears in some element of controller itself, controller can be found and report to the police, and does not make device out of service fully simultaneously, after the fault restoration, can resume operation at an easy rate.

The effect that experiment may reach: along with the raising of carrier frequency, the harmonic content in the output voltage is more and more littler, is increased to after the certain value but work as carrier frequency, and it is not obvious to the effect that reduces the harmonic content in the output voltage to increase carrier frequency again.Can increase the switching loss of device owing to carrier frequency is too high on the contrary.Simultaneously, load reactance increases, and makes the increase of load reactive power cause load bus voltage to descend, and STATCOM and control system thereof are by detecting this variation, and control STATCOM self compensating system is idle, and voltage is recovered.Because the influence of impact load, make the voltage on the motor bus that bigger decline be arranged, but STATCOM and control system thereof can be carried out dynamic passive compensation immediately, make the very fast recovery of busbar voltage, guarantee that motor speed is unlikely down with too much, and it is returned near the rated speed very soon.

Claims (7)

1. STATCOM control method based on the switched system theory is characterized in that this method comprises:

1st, analyze the main circuit topological structure of STATCOM device, determine to comprise the Mathematical Modeling of unit-Infinite bus system of STATCOM;

2nd, determine to comprise the third-order model of generator in unit-Infinite bus system of STATCOM, and the power system state equation and the output equation that contain STATCOM;

3rd, with the nonlinear model linearisation of STATCOM;

4th, determine the H of STATCOM _∞The design procedure of robust controller Mathematical Modeling and Robust Controller for Excitation of Generator;

5th, determine to form based on the structure of the The whole control system of the STATCOM of DSP.

2. method according to claim 1 is characterized in that the Mathematical Modeling of unit-Infinite bus system of the described STATCOM of comprising is:

$\left\{\begin{array}{c}\stackrel{.}{\mathrm{\δ}}=\mathrm{\ω}\\ M\stackrel{.}{\mathrm{\ω}}+\mathrm{D\ω}=P_m-(\frac{E_q^2}{X_L}\sin \mathrm{\δ}-\frac{1}{2}{E}_q{I}_{\mathrm{CR}}\sin \frac{\mathrm{\δ}}{2})\end{array}\right.$

In the formula, δ is a generator's power and angle, and ω is a rotor velocity, P _mBe generator input mechanical output, E _qHand over the axle electromotive force for generator, D is the unit damping constant, and M is an inertia constant of a set, X _LBe line reactance, I _CRBe the reactive power compensation electric current.

3. method according to claim 1 is characterized in that the third-order model of described generator is:

$\left\{\begin{array}{c}\stackrel{.}{\mathrm{\δ}}=\mathrm{\ω}\\ \stackrel{.}{\mathrm{\ω}}=-\frac{D}{M}\mathrm{\ω}+\frac{{\mathrm{\ω}}_0}{M}(P_m-P_e)\\ E_q^{\′}=-\frac{1}{T_{d0}^{\′}}{E}_q+\frac{1}{T_{d0}^{\′}}{E}_f\end{array}\right.$

In the formula, δ is a generator's power and angle, and ω is a rotor velocity, P _mBe generator input mechanical output, P _eBe generator active power, D is the unit damping constant, and M is an inertia constant of a set, E ' _qFor generator is handed over axle (q-axle) transient potential, E _qFor generator is handed over axle electromotive force, E _fBe generator excitation winding equivalent potential, T ' _DoBe d-axis transient state open circuit time constant.

4. method according to claim 1 is characterized in that power system state equation and the output equation of the described STATCOM of containing is respectively:

Make system mode vector x=[x ₁x ₂x ₃] ^T=[δ ω E ' _q] ^T, the input u=u of system _f, system exports y=δ, can draw the state equation of system:

$\stackrel{.}{x}=f\left(x\right)+g\left(x\right)u$

F (x)=[f wherein ₁(x) f ₂(x) f ₃(x)] ^T, g (x)=[0 0 g ₃] ^T

$f_1\left(x\right)={x_2,f}_2\left(x\right)=-\frac{D}{M}{x}_2+\frac{{\mathrm{\ω}}_0}{M}(P_m-\frac{V_1}{x_{\mathrm{d\Σ}}^{\′}}{x}_3\sin x_1)$

$f_3\left(x\right)=-\frac{1}{T_{\mathrm{do}}^{\′}}[x_3-(X_d-X_d^{\′})\frac{x_3-V_1\cos x_1}{X_{\mathrm{d\Σ}}^{\′}}],g_3=\frac{k_c}{T_{d0}^{\′}};$

The output equation of system is:

y＝h(x)＝x ₁。

5. method according to claim 1 is characterized in that the model after the nonlinear model linearisation of STATCOM is:

${\stackrel{.}{z}}_{123}={\mathrm{Az}}_{123}+B_{2}v+B_1{w}^{\′}$

${\stackrel{.}{z}}_4=a(z_{123},z_4)+b\left(w\right)$

y＝Cz ₁₂₃

Z wherein ₁₂₃=[z ₁z ₂z ₃] ^T, v=[v ₁v ₂] ^T, w '=[w ₁W ' ₂] ^T=[w ₁W ' ₂(w ₁, w ₂)] ^T

6. method according to claim 1 is characterized in that the H of described STATCOM _∞The robust controller Mathematical Modeling is:

$v_{1*}=-\frac{1}{{2\mathrm{\ϵ}}^2}\underset{i=1}{\overset{4}{\mathrm{\Σ}}}{p}_{2i}{z}_i,$ $v_{2*}=-\frac{1}{2{\mathrm{\ϵ}}^2}\underset{i=1}{\overset{4}{\mathrm{\Σ}}}{p}_{i4}{z}_i.$

7. method according to claim 1 is characterized in that the design procedure of described Robust Controller for Excitation of Generator is:

Step 1, the state-space model that provides system such as following formula (1) are described its uncertainty to (4), and analyze the uncertain boundary that it satisfies:

v _f＝I _q[k _cu _f-(X _d-X′ _d)I _d]+T′ _doQ _eω-P _m(2)

In the formula

$\mathrm{\μ}\left(t\right)=\frac{1}{{T^{\′}}_{d0}}-\frac{1}{{T^{\′}}_{d0}+\mathrm{\Δ}{T^{\′}}_{d0}},$ ${T^{\′}}_{d0}+{T^{\′}}_{d0}=\frac{{X^{\′}}_{\mathrm{d\Σ}}+\mathrm{\Δ}{X}_L}{X_{\mathrm{d\Σ}}+\mathrm{\Δ}{X}_L}{T}_{d0}$

Δ T ' _D0With Δ X _LRepresent T ' respectively _D0And X _LIn uncertainty, simultaneously, have

$T=\frac{{V^2}_t}{X_{\mathrm{d\Σ}}},$ $T+\mathrm{\ΔT}=\frac{{(V_t+\mathrm{\Δ}{V}_t)}^2}{{X^{\′}}_{\mathrm{d\Σ}}}$

Can be able to the lower linear model thus

$\stackrel{.}{\mathrm{\δ}}\left(t\right)=\mathrm{\ω}\left(t\right)$

$\stackrel{\·}{\mathrm{\ω}}\left(t\right)=-\frac{D}{M}\mathrm{\ω}\left(t\right)-\frac{{\mathrm{\ω}}_0}{M}\mathrm{\Δ}{P}_e\left(t\right)$

$\mathrm{\Δ}{\stackrel{\·}{P}}_e\left(t\right)=-[\frac{1}{{T^{\′}}_{d0}}+\mathrm{\μ}\left(t\right)]{\mathrm{\ΔP}}_e\left(t\right)+[\frac{1}{{T^{\′}}_{d0}}+\mathrm{\μ}\left(t\right)]v_f\left(t\right)+[\frac{1}{{T^{\′}}_{d0}}+\mathrm{\μ}\left(t\right)]{{\mathrm{\ΔT}}^{\′}}_{d0}{Q}_e\left(t\right)\mathrm{\ω}\left(t\right)+(T+\mathrm{\ΔT})\mathrm{\ω}\left(t\right)+({E^{\′}}_q{V}_t/{{\stackrel{.}{X}}^{\·}}_{d0})\sin \mathrm{\δ}\left(t\right)$

Definition status vector x (t)=[δ (t) ω (t) Δ P _e(t)] ^T, and the suffered interference of taking into account system model

W=[w ₁w ₂] ^T, above-mentioned inearized model can be write as

$\stackrel{\·}{x}\left(t\right)=[A+\mathrm{\ΔA}]x\left(t\right)+[B_2+\mathrm{\Δ}{B}_2]v_f\left(t\right)+B_{1}w\left(t\right)+\mathrm{\ΔGg}\left(x\right)---\left(4\right)$

z＝Cx (5)

Wherein

$A=\left(\begin{array}{ccc}0& 1& 0\\ 0& -\frac{D}{M}& -\frac{{\mathrm{\ω}}_0}{M}\\ 0& 0& -\frac{1}{{T^{\′}}_{d0}}\end{array}\right),\mathrm{\ΔA}=\left(\begin{array}{ccc}0& 0& 0\\ 0& 0& 0\\ 0& \mathrm{\β}& -\mathrm{\μ}\left(t\right)\end{array}\right),C=I$

$B_2={\left[\begin{array}{ccc}0& 0& \frac{1}{{T^{\′}}_{d0}}\end{array}\right]}^T,$ ${\mathrm{\ΔB}}_2={\left[\begin{array}{ccc}0& 0& \mathrm{\μ}\left(t\right)\end{array}\right]}^T,B_1={\left[\begin{array}{ccc}0& 1& 0\\ 0& 0& 1\end{array}\right]}^T---\left(6\right)$

$\mathrm{\β}=[\frac{1}{{T^{\′}}_{d0}}+\mathrm{\μ}\left(t\right)]{{\mathrm{\ΔT}}^{\′}}_{d0}{Q}_e+(T+\mathrm{\ΔT})---\left(7\right)$

$\mathrm{\ΔG}={\left[\begin{array}{ccc}0& 0& \mathrm{\γ}\end{array}\right]}^T,\mathrm{\γ}=\frac{{E^{\′}}_q\stackrel{\·}{V_t}}{{X^{\′}}_{\mathrm{d\Σ}}},g\left(x\right)=\sin \mathrm{\δ}---\left(8\right)$

μ (t), Δ T, Δ T ' _D0Bounded, thereby β also is a bounded; By above processing, the dynamic model that comprises the generator in unit-infinitely great electric power system of STATCOM has changed into one and has comprised multiple probabilistic linear system, promptly mixes these uncertainties of uncertain system and comprises Δ A, Δ B ₂The expression parameter uncertainty, by B ₁The disturbance uncertainty of expression, and the interconnected uncertainty of representing by Δ G;

Step 2, uncertain matrix is carried out STRUCTURE DECOMPOSITION;

These uncertainties can be done following decomposition

ΔA(t)＝LF(t)E ₁ (9)

ΔB ₂(t)＝LF(t)E ₂ (10)

ΔG(t)＝L′F′(t)E′(11)

Wherein

$\left.\begin{array}{c}L={\left[\begin{array}{ccc}0& 0& {\left|\mathrm{\μ}\right|}_{\max }\end{array}\right]}^T,F\left(t\right)=\left[\begin{array}{ccc}0& \frac{\mathrm{\β}}{{\left|\mathrm{\β}\right|}_{\max }}& -\frac{\mathrm{\μ}}{{\left|\mathrm{\μ}\right|}_{\max }}\end{array}\right]\\ E_1=\mathrm{diag}\{1,\frac{{\left|\mathrm{\β}\right|}_{\max }}{{\left|\mathrm{\μ}\right|}_{\max }},1\},E_2={\left[\begin{array}{ccc}0& 0& -1\end{array}\right]}^T\\ L^{\′}={\left[\begin{array}{ccc}0& 0& {\left|\mathrm{\γ}\right|}_{\max }\end{array}\right]}^T,F^{\′}\left(t\right)=\left[\frac{\mathrm{\γ}}{{\left|\mathrm{\γ}\right|}_{\max }}\right],E^{\′}=\left[1\right]\end{array}\right\}---\left(12\right)$

Satisfy following uncertain boundary

F ^T(t)F(t)≤I，F′ ^T(t)F ^T(t)≤I (13)

And || g (x) ||≤|| Wx||, W=[1 0 0] (14)

And

Consider the effect of generator forced exciting in addition, under severe case, excitation ceiling voltage multiple is 5, can get

$\left|\mathrm{\γ}\right|\≤\frac{4}{{T^{\′}}_{d0}{|}_{\min }}{P}_e{|}_{\max }---\left(16\right)$

Step 3, the suitable symmetric positive definite matrix Q of selection, structure algebraically Riccati equation;

$A^{T}P+\mathrm{PA}+P(B_1{B}_1^T+r^{-2}L{L}^T+{\mathrm{\λ}}^{-2}{L}^{\′}{L}^{\′T})P+r^2{E}_1^T{E}_1+W^{T}W+C^{T}C$

$-r^{-2}{(B_2^{T}P+E_2^T{E}_1)}^T{R}^{-1}(B_2^{T}P+E_2^T{E}_1)+Q=0$

Step 4, respectively according to 0＜r, λ＜1 and λ ²E ' ^TThe principle of E '＜I is selected parameter r, λ, and at this moment, Riccati equation is separated;

Step 5: find the solution Riccati equation, get its steady-state solution P, can obtain the robust controller of system.

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